You're describing what is actually going on in the real world. VCs are competing at Demo Day and valuations rise. Some think it is too expensive and avoid it.

1 on 11 isn't as realistic, because the VC would compete by wanting to put in more money. So 3 on 11 to 3 on 30.

The point of this post is to illustrate the math, but most importantly the second half is to show that this math isn't quite the right way to look at it. It is instructive to those that don't know much about this stuff.

I don't think a more complicated scenario would help explain this. For example, I left out option pools.